Business Finance · Capital structure and dividend policy

Modigliani-Miller Capital Structure Theory: Propositions With and Without Tax

Updated 11 October 2026 · Fact-checked

Modigliani-Miller (MM) theory shows when capital structure changes firm value. Without tax, in perfect markets, value does not depend on gearing, and cost of equity rises with gearing. With corporate tax, debt adds a tax shield worth Tc × D, so value rises with debt. You solve questions by applying the correct formula set.

Understand Modigliani-Miller Capital Structure Theory

Capital structure is the mix of debt and equity a firm uses to finance its assets. The key question is: can a firm raise its value just by changing this mix? MM answered this with a clean model, so you can see exactly which real-world features make the mix matter.

MM without tax (perfect markets). Assume no taxes, no transaction costs, no bankruptcy costs, and that investors and firms borrow at the same risk-free rate. Assume also that the firm's operating cash flows do not change with its financing. Proposition 1 says the value of a geared firm equals the value of an ungeared firm with the same business risk: VG = VU. The reason is arbitrage. If two firms had the same cash flows but different values, investors could use home-made gearing to buy the cheaper one and make a risk-free profit. Prices would move until values were equal.

Proposition 2 says the cost of equity rises as gearing rises. Debt is cheaper than equity, but adding it makes equity riskier. The rise in the cost of equity exactly offsets the cheaper debt. So the WACC stays constant and equals the ungeared cost of equity.

MM with corporate tax. Interest on debt is tax-deductible, so debt saves tax. If debt is permanent, the tax shield has a present value of Tc × D. Proposition 1 becomes VG = VU + Tc × D. Value rises with debt, and in the pure model the firm is best at nearly 100% debt. WACC falls as gearing rises. Proposition 2 still says cost of equity rises with gearing, but more slowly because of the tax shield.

Why it matters. The model is a benchmark. Real firms face bankruptcy costs, agency costs, personal taxes and information differences. These explain why firms do not borrow almost 100%, and they link to trade-off theory and optimal gearing. Be ready to state the assumptions and say which one is relaxed when the conclusion changes.

Key rules to remember

MM Proposition 1 (no tax): VG = VU = EBIT-based cash flow ÷ ke(U); Value is independent of gearing. For a perpetual cash flow X, VU = X ÷ ke(U), where ke(U) is the ungeared cost of equity.
MM Proposition 2 (no tax): ke(G) = ke(U) + (ke(U) − kd) × (D ÷ E); D and E are market values. Assumes debt is risk-free or its cost is kd with no change in risk. ke rises linearly with D ÷ E.
WACC (no tax): WACC = ke(G) × E ÷ (D + E) + kd × D ÷ (D + E) = ke(U); WACC is constant at all gearing levels in the no-tax case.
MM Proposition 1 (with corporate tax): VG = VU + Tc × D; Assumes permanent debt with fixed amount D. Tc is the corporate tax rate. Tc × D is the present value of the tax shield.
MM Proposition 2 (with corporate tax): ke(G) = ke(U) + (ke(U) − kd) × (1 − Tc) × (D ÷ E); The (1 − Tc) factor makes the rise in ke slower than in the no-tax case.
WACC (with corporate tax): WACC = ke(G) × E ÷ (D + E) + kd × (1 − Tc) × D ÷ (D + E) = ke(U) × (1 − Tc × D ÷ (D + E)); WACC falls as gearing rises. Use the second form for a quick check.
Ungeared value with tax: VU = X × (1 − Tc) ÷ ke(U); X is perpetual annual pre-tax operating earnings of the ungeared firm. ke(U) is the cost of equity of the ungeared firm.

How to solve Modigliani-Miller Capital Structure Theory questions

Use this method for any MM question, numerical or written.

1Read the assumptions. Note whether tax is present and whether debt is permanent and risk-free or has cost kd.
2Decide which set applies: no-tax formulas or with-tax formulas.
3Find the ungeared value VU or the ungeared cost of equity ke(U) first. Everything else is built from it.
4Compute the geared value: VG = VU for no tax, or VG = VU + Tc × D with tax.
5Find the equity value as E = VG − D. Use market values, not book values, for D and E.
6Find ke(G) from Proposition 2, then check that WACC matches the expected result (constant, or lower with tax).
7State the conclusion in words: does gearing affect value, and why. Mention the key assumption behind it.
8If the question asks for real-world factors, add bankruptcy costs, agency costs and personal tax as reasons for a limit on debt.

Quickest way: Shortcut: use VU, Tc × D and the WACC check

When to use it: Use this for MCQs and short numerical parts where you need a fast answer and a way to check it.

No tax: value does not change. Only ke changes, using ke(U) + (ke(U) − kd) × D ÷ E.
With tax: add Tc × D to value. Subtract D to get equity.
Check with WACC: with tax, WACC = ke(U) × (1 − Tc × D ÷ V). If your ke(G) does not reproduce this WACC, recheck.
In MCQs, eliminate options that say value falls with gearing or WACC rises with gearing in the pure MM model.

Common mistakes in Modigliani-Miller Capital Structure Theory

Saying that gearing has no effect on cost of equity in the no-tax case.
Students remember that value and WACC are unchanged and assume everything is unchanged.
Fix: Remember that ke rises with gearing. It is the rise in ke that keeps WACC constant.
Using (1 − Tc) on ke(U) − kd missing in Proposition 2 with tax.
Students copy the no-tax formula and forget the tax adjustment.
Fix: Write both formulas side by side and note that the with-tax version has (1 − Tc) multiplying the D ÷ E term.
Adding the tax shield as Tc × interest rather than Tc × D.
Students confuse the annual saving with its present value.
Fix: Annual saving is Tc × kd × D. Discounted at kd as a perpetuity, its present value is Tc × D.
Using book values of debt and equity in D ÷ E.
Book values are easier to find in the question.
Fix: MM formulas use market values. Use VG − D for equity if no market value of equity is given.
Concluding that firms should be 100% debt financed.
The with-tax model suggests value always rises with debt.
Fix: State that the result relies on no bankruptcy or agency costs. Real firms balance the tax shield against those costs.
Forgetting the assumptions when answering a discussion question.
Students focus on formulas.
Fix: Open with the assumptions: perfect markets, no tax or tax only on corporates, same borrowing rate, no bankruptcy costs, fixed operating cash flows.

Worked examples

Example 1

Firm U is ungeared with perpetual annual earnings of ₹60 crore before interest and has cost of equity 12%. Firm G has identical operations and ₹200 crore of permanent debt at 8%. There are no taxes and MM assumptions hold. Find (a) the value of G, (b) the value of G's equity, (c) G's cost of equity, and (d) G's WACC.

Show the solution

VU = 60 ÷ 0.12 = ₹500 crore.
(a) With no tax, VG = VU = ₹500 crore.
(b) E = VG − D = 500 − 200 = ₹300 crore.
(c) ke(G) = 12% + (12% − 8%) × (200 ÷ 300) = 12% + 4% × 0.6667 = 12% + 2.667% = 14.667%.
(d) WACC = 14.667% × (300 ÷ 500) + 8% × (200 ÷ 500) = 8.8% + 3.2% = 12.0%.

Answer: (a) ₹500 crore. (b) ₹300 crore. (c) about 14.67%. (d) 12%, equal to the ungeared cost of equity.

Example 2

Using the same firms as above, now assume corporate tax of 30% on all earnings and that the debt is permanent. Earnings of ₹60 crore are before interest and tax, and ke(U) is still 12% on after-tax earnings. Find (a) VU, (b) VG, (c) E for G, (d) ke(G) and (e) WACC for G.

Show the solution

(a) VU = 60 × (1 − 0.30) ÷ 0.12 = 42 ÷ 0.12 = ₹350 crore.
(b) Tax shield = 0.30 × 200 = ₹60 crore. VG = 350 + 60 = ₹410 crore.
(c) E = 410 − 200 = ₹210 crore.
(d) ke(G) = 12% + (12% − 8%) × (1 − 0.30) × (200 ÷ 210) = 12% + 4% × 0.7 × 0.95238 = 12% + 2.667% = 14.667%.
(e) WACC = 14.667% × (210 ÷ 410) + 8% × 0.7 × (200 ÷ 410) = 7.512% + 2.732% = 10.244%.
Check: ke(U) × (1 − Tc × D ÷ V) = 12% × (1 − 0.3 × 200 ÷ 410) = 12% × (1 − 0.14634) = 12% × 0.85366 = 10.244%. This matches.

Answer: (a) ₹350 crore. (b) ₹410 crore. (c) ₹210 crore. (d) about 14.67%. (e) about 10.24%, lower than the 12% ungeared cost, because of the tax shield.

Exam tips

Write the assumptions in the first two lines of any discussion answer. Markers look for them.
In numerical questions, find VU first and keep a running check using the WACC formula.
Label each of D, E and V clearly as market values. Keep units in ₹ crore or ₹ lakh consistent.
When asked about real-world limits, give at least three: bankruptcy costs, agency costs and personal tax effects. Link each to why debt is limited.
For MCQs, remember the direction of change: ke rises with gearing in both cases, WACC is flat without tax and falls with tax.

Practice questions from Capital structure and dividend policy

Modigliani-Miller Capital Structure Theory in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Modigliani-Miller Capital Structure Theory: frequently asked questions

What is the difference between MM with and without tax?

Without tax, firm value and WACC do not change with gearing. With corporate tax, interest is deductible, so value rises by Tc × D and WACC falls as gearing rises. In both cases the cost of equity rises with gearing.

How does gearing affect cost of equity in MM theory?

Shareholders face more financial risk as debt rises, so they demand a higher return. Without tax, ke(G) = ke(U) + (ke(U) − kd) × D ÷ E. With tax, the increase is smaller because of the (1 − Tc) factor.

Why does MM with tax suggest 100% debt?

The model counts the tax shield but ignores bankruptcy and agency costs. Each extra rupee of permanent debt adds Tc rupees of value, so the model keeps rewarding debt. Real firms stop where the extra costs of distress outweigh the tax benefit.

Do I need to remember the proofs for the IAI exam?

Focus on the results, the formulas and the assumptions. You should be able to explain the arbitrage idea in words. Numerical use of the formulas and a clear discussion of limits are the most common ways the topic is tested.